Question

A block of mass $10kg$ is moving in x-direction with constant speed of $10m/s$. It is subjected to a retarding force $F=0.1x$ joule/metre during its travel from $x=20m$ to $x=30m$. Its final K.E will be:

• A. $475J$
• B. $450J$
• C. $275J$
• D. $250J$

Answer 1

The correct option is A $475J$

Given : Retarding force $F=0.1x$ for $20<x<30$

Mass of the block $m=10kg$

$\therefore$ $F=m(-a)$ (- sign shows retardation)

$ma=-0.1x$

$\left(10\right)v\frac{dv}{dx}=-0.1x$

${\int }_{10}^{v}vdv=-0.01{\int }_{20}^{30}xdx$

$\frac{v^2}{2}{|}_{10}^v=-0.01\times \frac{x^2}{2}{|}_{20}^{30}$

$v^2-{10}^2=-0.01\times ({30}^2-{20}^2)$ $⟹$ $v^2=95$

Final kinetic energy $E=\frac{1}{2}m{v}^2=\frac{1}{2}\times 10\times 95=475$ $J$